John Henry won the battle, but lost the war. How is being outcalculated by a computer news? Just because it's a hard problem?

It involves a certain amount of intuition. You'd always use a computer to optimize a trajectory, but picking the overall approach to be used requires some educated guessing. You can visit any other planets along the way, or their moons, and you can visit them at an optimal point along their orbit or somewhere that is non-optimal (from the standpoint of that particular encounter). You can launch today at one cost, or wait 20 years and maybe launch at a cheaper cost.

So, the current approach is generally to have physicists come up with a couple of basic plans, then use computers to optimize each one, and then see which works best, or perhaps iterate.

Looking at it another way, this is similar to any other problem where you're trying to find the lowest minima in a function that has many local ones. Finding the nearest minima is easy - finding the best is much harder.